Structure-from-Motion and Wavelet Decomposition
for outcrop analysis
Christopher Gomez1,*
1. University of Canterbury, College of Sciences, Department of Geography. Private Bag 4800,
Christchurch 8140, New Zealand.
* corresponding author: christopher.gomez@canterbury.ac.nz
Technical Paper in HAL Archives en Ligne
technological state, some information
Abstract
collected in the field can’t be measured
The
rise
of
numerical
methods
in
numerically. Therefore the authors have
geological sciences, including volcanic
suggested that photogrammetry based
surface and subsurface analysis offers the
algorithms could help extend the analysis
21st century the opportunity to work on
potential from one localized control point
large datasets and refine the level of
– where the researcher can sample,
details collected. At the same time,
measure and describe an outcrop - to a
outcrops are still the base of numerous
larger area. Hence information from one
near-surface analysis, especially on active
sample could be extended to long transects
volcanoes and only few progress has been
and show large/progressive horizontal
made around the data-collection method,
variations that can’t be easily identified
if not using expensive tools such as
from manual work.
terrestrial laser scanners. In the present
contribution, the authors have investigated
1. Introduction
the potential of the photogrammetric
method SfM-MFS (Structure from Motion
Outcrops are arguably one of the most
and Multiple-View Stereophotogrammetry
important sources of data to study the
), in order to improve the manual process
subsurface
of outcrop analysis, and they have also
geomorphology of volcanic environments.
investigated the use of wavelets and
Outcrop analysis is essential – for instance
spatial analysis techniques – usually used
– for calibrating several non-destructive
in GIS analysis - applied to a vertical
methods, such as ground-penetrating radar
surface. Results have proven that SfM-
(GPR), in volcanic environments where
MVS can record precise 3D data from an
data
outcrop. The method also allows the
(Abrams and Sigurdsson, 2007; Cassidy et
construction of orthophotographs of the
al., 2009; Courtland et al., 2012; Finizola
outcrop, which can then be used for
et al., 2010; Gomez and Lavigne, 2009;
further image analysis. The usage of
Gomez et al., 2008, 2009, 2012; Gomez-
wavelets and other spatial algorithms have
Ortiz et al., 2006; Khan et al., 2007).
shown their ability to extract features and
Despite being a traditional technique,
variations in the grain-size from numerical
outcrop analysis has recently seen a
data. This study has also shown the limits
methodological
resurgence
of such techniques, as in the present
application
remote
geology
collection
of
can
and
be
the
challenging
with
sensing
the
(RS)
techniques,
such
as
close-range
2013) and the mechanisms of rock
hyperspectral imagery to map mineral
fragmentation
(Tatone
content (Buckley et al., 2013) and
2009).
terrestrial laser scanning, to describe
electromagnetic scattering on a surface and
millimeter to centimeter scale features
therefore plays an important role in remote
(Bellian et al., 2005).. Despite important
sensing interpretation (Beckmann and
gains in descriptive potential, exploration
Spizzichino, 1987). In this paper, we add
using these RS techniques has been
to the recent research on using remote-
relatively sparse, most probably because
sensing techniques for outcrop analysis.
the technical and financial aspects are still
Here we explore the question of
prohibitive, and the great majority deals
whether cost-effective remote sensing
with sub-horizontal surfaces rather than
data
sub-vertical ones (e.g. Heritage and Milan,
accurately describe surface texture of
2009). Moreover, the contributions – to
volcanic outcrops.
Surface
and
texture
acquisition
can
Grasselli,
also
be
controls
used
to
date – deal mostly with data acquisition
and
handling
rather
than
obtaining
We: (1) present Structure–from-Motion
parameters from which one could derive
associated
indicators on the nature of the studied
Stereophotogrammetry
material in an automated manner (e.g.
low-cost alternative to terrestrial laser
Giaccio et al., 2002).
scanning
with
(Morgenroth
Multiple-View
(SfM-MVS),
and
a
Gomez,
2014)and describe how it could be applied
One potential direction that can be
to outcrop analysis; and (2) test various
explored is the analysis of outcrop surface
surface texture indicators and the use of
texture (or surface roughness), which can
wavelet
be
roughness analysis, in order to determine if
a
key
proxy
for
environmental
decomposition
for
surface
processes. This is particularly true in the
these
field
automatic recognition of granularity and
of
agriculture
where
surface
roughness gives indications on wind
indicators
could
be
used
for
derivation of grain-size variations.
deflation, runoff and water absorption,
even playing an important part in soil biota
In
and gas exchanges (Vidal Vazquez et al.,
known as Structure-and-Motion) was first
2005).
used
developed in the field of computer-vision
variations of surface texture to characterize
engineering (Ullman, 1979). It has since
Geologists
have
also
different volcanic deposits (Bretar et al.,
1979,
Structure-from-Motion
(also
developed
into
a
valuable
tool
for
PhotoScan®-Professional (Agisoft LLC,
generating 3D models from 2D imagery
St. Petersburg, Russia). Although the
(Szelinski,
procedures described in this study are
2011),
notably
with
the
development of software with Graphical
achievable using various free-ware options,
User
Traditional
the decision to use PhotoScan-Professional
photogrammetry requires a series of
software was made because it couples SfM
identifiable points to be present in at least
technology with multi-view
two photographs
stereophotogrammetry (MVS) algorithms
Interfaces.
and,
perhaps
more
importantly, known values of camera
in a user-friendly interface. Using this
projection,
combined SfM-MVS approach, the
distortion,
position,
and
orientation (Robertson and Cipolla, 2009).
software retrieves an initial set of sparse
By contrast, SfM uses algorithms to
points from matching features (SfM) and
identify matching features in a collection
then increases the point-cloud density to
of
improve the reconstruction of the
overlapping
digital
images,
and
calculates camera location and orientation
overlying 3D mesh using MVS technology
from the differential positions of multiple
(Agisoft Photoscan-PRO, 2012; James and
matched features (Fisher, et al., 2005;
Robson, 2012; Verhoeven, et al., 2012).
Quan, 2010; Szeliski, 2011). Based on
these calculations overlapping imagery can
In
order
to
numerically
be used to reconstruct a 3D model of the
variations of a surface from an ideal
photographed object or scene. Where
general shape, a series of tools are
relative projection geometry and camera
available,
position are known the values can be
statistical indicators to more complex
integrated into the SfM reconstruction to
fractal-based (Bretard, et al., 2013) and
improve the calculation productivity and
wavelet-based analysis (Gomez, 2012)
accuracy of the model (Agisoft Photoscan-
allowing
PRO, 2012).
(Gomez, 2013).During the last 10 years,
A number of desktop and browser-based
the use of wavelet analysis in earth-
SfM software packages are freely available
sciences has increased concomitantly with
for generating 3D scenes from digital
the increasing availability of numerical
photographs (e.g. Snavely, et al., 2006;
data. It has especially benefited from the
Snaveley, 2010; AperoMicMac: Bretard,
study of time-series for the determination
et al., 2013). However, this study used a
of different frequencies and momentums
commercial software program, Agisoft
(e.g. Andreo et al., 2006; Partal and Küçük
spanning
measures
from
at
study
the
descriptive
various
scales
2006; Rossi et al., 2009). Analyses of
space-scale data with wavelet - although
2. Location
more scarce in earth-sciences – are also on
the rise (e.g. Audet and Mareschal, 2007;
Japan is a volcanic archipelago that seats
Booth et al., 2009; Lashermes et al.,
on the Pacific Ring of Fire and it is
2007), eventually following the influence
arguably one of the most tectonically and
of research in medical imagery, which has
volcanically active regions in the world.
been
for
Numazawa Volcano is located on the main
topographical analysis for instance (e.g.
island of Japan, Honshu, in the western
Langenbucher et al., 2002).
part of Fukushima prefecture and about 50
Wavelets allow the decomposition of a
km from the volcanic front defined by
signal into a set of approximations, which
Sugimura (Sugimura, 1960; Yamamoto,
is
a
2007; Kataoka et al., 2008). Numazawa
combination of different scales. Wavelet
Volcano has developed on the edge of the
analyses use a short-term duration wave as
Uwaigusa caldera complex (Yamamoto
a kernel function in an integral transform.
and Komazawa, 2004) to reach a present
There are several types of wavelet, which
altitude of 1100 m a.s.l. A 2 km wide and
are named after their inventors: e.g. Morlet
~100 m deep lake has formed within the
wavelet, Meyer wavelet. Based on the
caldera
shape of the series/function that needs to
volcaniclastic
be analyzed, the appropriate mother
Numazawa volcano are:the 110 k.a.
wavelet is scaled and translated (daughter
Sibahara pyroclastic deposits; the 71 k.a
wavelet), allowing the detection of the
Mukuresawa lava dome; the 45 k.a
different frequencies of a signal at
Mizunuma pyroclastic-flow deposits; the
different time (Torrence and Compo 1998;
Sozan lava dome of 43 k.a; the Maeyama
Schneider
This
lava dome of 20 k.a and the Numazawako
mathematical transform can be very useful
eruption of 5 k.a (Yamamoto, 2007).
to study surface variations of large-scale
Kataoka et al. (2008) have described in
topography or localized surface texture
details the Numazawako eruption and the
Wavelet is a well-fitted tool for separating
geomorphic impacts around the volcano,
spectral components of topography (i.e.
including the flood terraces in the Tadami
working on different scales of a single
river, from which the material used in the
object), because it gives both the spatial
present contribution has been extracted
and the spectral resolution.
(Cf. Fig. 9 in Kataoka et al., 2008). The
widely
hierarchically
and
using
wavelet
organized
Farge,
2006).
in
.
Chronologically,
deposits
generated
the
by
290 cm high x 85 cm wide outcrop-peel
cloud and camera location calculated by
was extracted from hyperconcentrated-
SfM. The 3D mesh was exported as both a
flow deposits with multiple inversely
vector model and a pixel based map (Fig.
graded bed sets, rich in rounded pumices.
2).
The matrix is dominated by coarse sand to
Data were then exported into (1) the GIS
pebble size material. The peel is part of a
environment ArcGIS® (ESRI, Redlands,
15 m thick unit that lied on top of debris-
CA,
flow deposits.
(MathWorks, Inc, Natick, MA, USA)
USA)and
(2)
the
MATLAB®
programming environment (Fig. 2). In the
GIS environment, the 3D surface created
3. Method
from SfM-MVS was loaded as a single
For the present study, a sandy to gravely
layer and transformed into a tiff file that
material from Numazawa Volcano (Japan)
can be recognized as a 3 level matrix in
has been digitally acquired and analyzed.
Matlab. The dataset was then transfered
The digital data has been collected using a
into the Matlab programming environment
point and shoot digital camera (Canon
to conduct the examination and measures
cybershot), by ‘hovering’ over the outcrop
of
taking 170 photographs from a distance of
using a series of different mathematical
10 to 40 cm. The method for image
tools: (a) wavelet decomposition; (b)
acquisition may differ depending on the
arithmetic average roughness; and (c)
algorithm used (e.g. Fig. 1 in Westoby,
proximity
2012). In this study, photographs were
maximum negative variation in a square of
taken to maximize the overlap such that
2x2 cm. The algorithms were implemented
features of the outcrop were captured by
using ‘cellular automata-type’ series of
multiple photographs.
scripts. The acquisition and processing
surface
texture-variations/roughness
analysis
of
positive
and
methods have been then discussed to
Using PhotoScan – professional, we
present the limits and potentials of the
applied the SfM technique to reconstruct a
different method.
point-cloud
based
solely
on
the
uncalibrated photographs, with tie-points
4. Results
of known location (x,y,z) in order to
constrain the point-cloud in 3D. We
4.1 Visual description from 3D digital
subsequently used the MVS technique to
outcrop
build a 3D surface from the 3D point-
Fig. 3 Outcrop reconstruction from the SfM-MVS derived collated orthorectified and scaled
referenced imagery. The outcrop representation on the left displays the main sedimentary
structures with mix-sand and coarse sand matrix (1) layers; and coarse-sand to small
pebbles matrix layers (2). Larger Pebbles – mostly pumices – of significant size were
individually recorded and measured with the visible L-axis (long-axis) and the visible area,
as displayed on the right representation of the outcrop.
Using the visual results of the SfM-MVS
in the outcrop, as they are mostly located
recomposition, a series of layers of coarse
in the superior half: all the clasts of L>51
sands to coarse sands and pebbles matrix
mm located between 145 cm and 290 cm
have been identified (Fig. 3). The layers of
height, and only 3 clasts of 36 mm < L <
coarser matrix also include larger clasts
50 mm are located in the bottom half of
that are mainly pumices as visually
the
identified from the digital outcrop. These
reconstruction can therefore yield useful
clasts have a main axis (L) of the range
information for a traditional outcrop visual
~10 to 80 mm (as measured from the 3D
analysis (Cf. visual in Fig. 4-a), but more
digital outcrop) and a visible surface of 8
importantly SfM-MVS also reconstructed
to 250 mm2 (Fig. 3). Mostly contained in
the surface ‘vertical topography’ of the
the layers of coarser matrix – except for
outcrop (Fig. 4).
outcrop.
The
SfM-MVS
visual
one large pumice located at 145 cm height
– the distribution of larger clasts is uneven
4.2 Haar-wavelet decomposition as a
tool to study micro-variations
The vertical topography derived from
decomposition (Fig. 4-c,d,e). The resulting
SfM-MVS has been extracted from a
variation is shown in Fig. 4-e, where only
virtual perfectly vertical plane , and
the
therefore one can observe a slight slant of
general sloping trend have been conserved.
6 cm along the 290 cm height of the
This transformation has put the emphasis
outcrop-peel, the bottom part extruding the
of the lower part of the outcrop where
most from the perfect vertical plane. In
numerous
order to perform localized analysis of the
were disappearing in the general slope
surface variations, the general slope of the
acceleration. In the upper part of the
surface has been subtracted using wavelet
outcrop
variations
independent
micro-topography
from
the
variations
Fig. 4 Detrending using wavelet. Transformation of the surface ‘topography’ obtained from
Structure From Motion. (a) Orthophotograph constructed from Structure from Motion; (b)
Surface variation, the 0 being the perfect vertical; (c) Surface extraction of the vertical
transect at the centre of the outcrop; (d) ‘topographic’ general trend as extracted by Haar
wavelet decomposition (Level 7 of a 7 scales decomposition); (e) Combination of the 4 lowest
level of wavelet decomposition minus the main trend at level 7 (e = L1+L2+L3+L4-L7). One
will note that (b) is only coded to 280 cm height as the upper part also includes the wood
frame around the peel, which creates strong micro-topographic variations spreading the
variation scale and thus limiting the graphic quality of the output.
just above and below the 500 sampling
strongly in the combined levels of the
point, one can observe - in Fig. 4-e – the
wavelet decomposition (Fig. 4-E) – have
strong variation of the signal and link them
created strong amplitude variations in the
to two units of coarser material including
lowest level of the wavelet decomposition
larger clasts of centimeter-scale (Fig. 4-a
(Fig. 5-H).
& Fig. 3).
Wavelet decomposition has shown to be a
Since the different levels of wavelet
useful tool to automate processes such as
decomposition are scale-related, we have
detrending and surface roughness patterns,
used the lowest level of the Haar-wavelet
but the reasons behind the signal micro-
decomposition (Fig. 5) in order to detect
variations
the finer micro-variations of the outcrop
limiting an automated recognition system
along 7 vertical transects equally spaced
based solely on wavelet decomposition.
can
have
various
sources
between 10 cm and 70 cm. This analysis
has yielded positive results with variations
4.3 Statistical and Spatial Analysis to
in the coarser units being clearly detected
detect
in ‘A’, ‘B’ and ‘F’ (Fig. 5). Local
variations
inclusions
of
larger
size
have
surface
roughness
micro-
also
influenced the signal (Fig. 5-C). In the
The indicators used in the present section
same
are
manner,
sandy
layers
without
normally
used
in
GIS
to
detect
inclusion of large clasts or pebbles have
microvariations
and
in
the
displayed smoother signal traces with
manufacturing industry. Although the
instrumentation and the scale are different
limited amplitude (Fig. 5-D). The signal
the underlying algorithms are similar. The
also reacted to microvariations that are not
first indicator tested is the arithmetic
due to grain-size variations, but linked to
roughness average (Ra), which gives
the fracture of the outcrop itself, such as
indications of the localized maximum
the desiccation holes and cracks (Fig 5-E)
variation
and those created during the transport of
computed over an average moving window
the outcrop-peel (Fig. 5-G). The effects of
of 2 cm2 has been successful at identifying
the micro-rills located at the bottom of the
rapid localized variations generated by
outcrop – and which did not appear
increased roughness due to the coarseness
(Fig.
6).
This
algorithm,
Fig. 5 Wavelet decomposition of the outcrop at level 1 (out of a 7 levels decomposition using
a Haar mother-wavelet). As the lowest level reacts to the shortest variations in space, this
analysis was performed to detect the microvariations (this lowest level is often considered as
the ‘white-noise’ in signal processing).
It calculates the root mean square of the
of the matrix (Fig. 6-b,d). It also
squared variation values from an ideal
succeeded at identifying smoother material
surface – in the present case the detrended
on the outcrop (Fig. 6-a,c,e) and defining
surface roughness.
their smaller scale variations. Indeed the
variation of coarse material is in the order
The result of the RMS shows the ability of
of x*10-3 m, while finer material varies in
the algorithm to detect and individualize
the order of x*10-4 m from local average
local variations, due here to the presence
variation (one will note that these later
of the centimeter-scale clast inclusions
variations are below the mm scale and
(Fig. 7-1&2), but it also detects quick
most certainly fall within the error of
variations such as the edge of a layer
margin of data acquisition).
slightly protruding from the rest of the
The second algorithm tested with a relative
outcrop (Fig. 7-3).
success is the RMS:
1
𝐿
[(𝐿 ∫0 𝑍(𝑥 )2 𝑑𝑥]1/2
Fig. 6 Arithmetic average roughness (Ra) extracted using a 2cm x 2cm moving average
detrending, which reduces the effects of large variation on the outcrop. (a & c) Ra of coarse
sand units; (b & d) Ra of coarser sand with gravels and centimetric clasts inclusions; (e) Ra
of coarse sand with several vertical erosional rill remnants. It is interesting to note that Ra
did not react to these variations (one will note that the scales of a,c and e are the same but b
and d differ in order to display the variations at different scales).
Fig. 7 RMS or square root of the square of local variation from the entire detrended surface.
This index allows finding elements that protrude locally from the surrounding, such as
isolated gravels in finer material, etc. The profile (a) is the reconstructed photograph using
textured SfM-MVS; the profile (b) is the surface microtopography from an idea vertical;
profile (c) is the dvar. On the three profiles box 1,2 and 3 have been drawn for regions of
interests
(see
the
text
for
full
comments
on
these
boxes).
processing and interpretation’ of data
Discussion
captured with a roughness-meter or even
The different algorithms using wavelet and
non-contact methods such as SfM-MVS or
spatial statistics techniques tested here on
TLS is possible, it is necessary to improve
the SfM-MVS derived data have shown
the speed of data processing for large-
their ability to produce measures of the
surface rock-faces. Based on the results
surface roughness. It also shows that the
obtained in the present study both a
SfM-MVS
decomposition using wavelet and a RMS
is
successfully
variations
a
method
capture
on
that
can
microtopographic
outcrops
even
at
could
improve
such
processing
and
the
produce a map of local micro-variations.
millimeter level. The intrinsic advantage
Other applications of the combination of
of this workflow is its low-cost (e.g. of
SfM-MVS
topographic application: Westoby et al.,
algorithms are numerous, as SfM-MVS,
2012) and the fact that anybody can go and
wavelet decomposition and the spatial
collect data for the scientist to process, as
analysis algorithms used in the present
it only requires standard overlapping
study are scale-independent. They can be
photographs from a low-cost, off-the-shelf
applied from the mountain-scale to the
camera. However, the surface roughness
micro-soil variation scale.
processing algorithms tested here are not
As pointed out by Westoby et al., (2012),
sufficiently developed to automate the
despite
process of recognizing layers of coarser
logistic demand, SfM-MVS is extremely
grain-size or the presence of larger
time-consuming during the processing
‘individuals’ in a series as they also reacts
process. Using a four core E7 at 2GhZ
to the imperfections of the outcrop.
CPU and 6GB RAM the SfM-MVS
process
Although
of
portability,low-cost
reached
almost
roughness
and
30
low-
hours
computing. This lengthy process could be
imperfections hamper the full-automation
reduced by diminishing the resolution of
of the process in the present study, the
the photographs, though this may result
behavior of these algorithms could be used
inloss ofdetail, then in the density of
to detect the imperfections on rock-faces,
keypoints and thus,the final quality of the
which Giaccio et al. (2002) measured
reconstructed surface may be deminished.
using a roughness-meter, and used as a
Working at a sub-centimeter to centimeter
proxy of erosion features invisible to the
level, it is therefore important to keep the
.
detection
surface
these
naked eye
the
with
Although the ‘manual
full-resolution of the photographs.
from a known outcrop or borehole in order
The development of this method, and the
to provide more spatially significant
need for powerful algorithms, and the
results.
hardware limitation are all symptomatic of
the recent shift in the technical paradigms
Conclusion
of geo-sciences, for which data is widely
SfM-MVS is a rapid method to collect
available, easy to collect (compared to ~30
very fine outcrop data in the field, and
years ago), and it is therefore less of a
could be extensively used on volcanoes,
challenge than the data-processing, too
because it would allow the preservation of
numerous to be effectively used in a timely
orthorectified and georeferenced outcrop
manner. This shift and the necessity to
morphologies and images, which would be
develop
extremely useful for comparisons after
appropriate
data
processing
algorithms is also perceptible in the
volcanic
evolutions,
especially
on
funding strategies like the late y.2013 NSF
volcanoes that change extremely quickly.
grant ‘EarthCube’, aiming to develop
Such extended dataset are therefore in
cyber-infrastructure in earth-sciences.
need of algorithms providing partial or
full-automation of some of the processing
Finally,
the limitations
of the data
steps.
It
appears
that
wavelet
processing method also highlight the fact
decomposition and RMS would provide a
that human experience and eyes in the
rapid insight on the location of coarser
field can’t be replaced by a fully
materials and individual outliers, while
automated system, as the present state of
arithmetic surface roughness would be
remote-sensing
and
more useful to detect units or layers that
processing alone doesn’t allow us to
are similar on an outcrop. Following the
extract all the necessary data. At present, it
present work, the next step will be the
is
SfM-MVS
retrieval of outdoor data and grain-size
acquisition method can be used as a
samples in order to find eventual linkages
complementary method. Indeed, traditional
between surface roughness indicators and
analysis and sampling could act as a
grain-size distribution.
most
likely
data
that
acquisition
the
control point for SfM-MVS, which would
be then able to expand the localized
knowledge
to
long
outcrops.
Such
‘ground-truthing’ is often used for GPR
studies, where the researcher can start
Acknowledgement
application
to
the
The authors are in debt to two anonymous
anisotropy
reviewers for their role in improving the
Geophysics Journal International 168,
manuscript and to the editor for a prompt
287-298.
in
the
elastic
thickness
Canadian
Shield.
and thoughtful handling of the manuscript.
Beckmann, P., Spizzichino, A., 1987. The
scattering of electromagnetic waves from
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